In designing touch-screen based user interfaces for remotely controlling a network-connected programmable thermostat, it is desirable to provide a high level of user-friendliness and intuitiveness. Additionally, when using a wireless communication technology over a computer network, it is desirable to impact network traffic as little as possible. Notably, the above-stated goals of user-friendliness, intuitiveness, and low network impact are shared with many different remote control scenarios, and it is indeed recognized that some progress has been made in the art toward these goals, as reflected, for example, in U.S. Pat. No. 8,239,784, WO 2012118626, and US20080084400, each of which is incorporated by reference herein. However, it has been found that remote control of an HVAC system brings about one or more unique combinations of issues that need to be simultaneously resolved, all the while continuing to provide user-friendliness and intuitiveness. By way of example, it has been found desirable to provide a remote control user interface for a thermostat in which the actual resultant control signals are judiciously tailored to protect the HVAC equipment from unwarranted over-controlling, reduce unnecessary network traffic, and prevent the waste of energy, while at the same time providing a user interface experience in which the user perceives a high degree of control, a sense that they are “in command”, of an intuitive and delightfully easy-to-use temperature control system.